Autoregulatory feedback loops occur in the regulation of molecules ranging from ATP to MAP kinases to zinc. Negative feedback loops can increase a system's robustness, while positive feedback loops can mediate transitions between cell states. Recent genome-wide experimental and computational studies predict hundreds of novel feedback loops. However, not all physical interactions are regulatory, and many experimental methods cannot detect self-interactions. Our understanding of regulatory feedback loops is therefore hampered by the lack of high-throughput methods to experimentally quantify the presence, strength and temporal dynamics of autoregulatory feedback loops. Here we present a mathematical and experimental framework for high-throughput quantification of feedback regulation and apply it to RNA binding proteins (RBPs) in yeast. Our method is able to determine the existence of both direct and indirect positive and negative feedback loops, and to quantify the strength of these loops. We experimentally validate our model using two RBPs which lack native feedback loops and by the introduction of synthetic feedback loops. We find that RBP Puf3 does not natively participate in any direct or indirect feedback regulation, but that replacing the native 3'UTR with that of COX17 generates an auto-regulatory negative feedback loop which reduces gene expression noise. Likewise, RBP Pub1 does not natively participate in any feedback loops, but a synthetic positive feedback loop involving Pub1 results in increased expression noise. Our results demonstrate a synthetic experimental system for quantifying the existence and strength of feedback loops using a combination of high-throughput experiments and mathematical modeling. This system will be of great use in measuring auto-regulatory feedback by RNA binding proteins, a regulatory motif that is difficult to quantify using existing high-throughput methods.